Multilevel workflow method to extract resistivity anisotropy data from three-dimensional induction measurements

ABSTRACT

A multi-step electromagnetic inversion method is provided for determining formation resistivity, anisotropy and dip. An electromagnetic logging tool is used to obtain non-directional, anisotropy, and directional (including symmetrized and anti-symmetrized resistivity measurements) in a formation using an electromagnetic logging tool. Bed boundaries of the formation are first identified. A horizontal resistivity profile is obtained using the non-directional resistivity measurements, and a vertical resistivity profile is obtained using the anisotropy resistivity measurements. The vertical resistivity profile is improved using the directional resistivity measurements, while dip values are also obtained via an inversion using the directional resistivity measurements. Then, an inversion for each of vertical resistivity, horizontal resistivity, dip values, and bed boundaries is performed using all of the non-directional, anisotropy, and directional resistivity measurements to obtain a formation model.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.12/888,232, filed Sep. 22, 2010, now U.S. Pat. No. 8,433,518, andentitled “Multilevel Workflow Method to Extract Resistivity AnisotropyData from 3D Induction Measurements”, which claims priority from U.S.Provisional Patent Application No. 61/326,287 filed Apr. 21, 2010 andfrom U.S. Provisional Patent Application No. 61/248,790 filed Oct. 5,2009, all of which are incorporated by reference herein in theirentirety.

BACKGROUND

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the subject matterdescribed and/or claimed below. This discussion is believed to behelpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentdisclosure. Accordingly, it should be understood that these statementsare to be read in this light, not as admissions of prior art.

The present disclosure relates generally to the field of electromagneticmeasurements of rock formation resistivity made by instruments disposedin wellbores drilled through rock formations. More specifically, thedisclosure relates to methods for determining resistivity, resistivityanisotropy and formation attitude (dip) using electromagneticmeasurements of the rock formations.

One of the major recent developments in well logging technology is theintroduction of electromagnetic measurements with three dimensional (3D)sensitivities. In so called “wireline” measuring systems (i.e., thoseconveyed through wellbores at the end of an armored electrical cable),3D electromagnetic induction measurements are designed primarily fordetecting resistivity anisotropy in vertical wells (see, e.g.,Krieghauser et al, A New Multicomponent Induction Tool to ResolveAnisotropic Formation, paper D presented at the 2000 41^(st) AnnualSPWLA Symposium, Salt Lake City, Utah, 30 May-3 June, and Rosthal, R.,Barber, T., Bonner, S., Chen, K. C., Davydycheva, S., Hazen, G., Homan,D., Kibbe, S., Minerbo, G., Schlein, R., Villegas, Wang, W., and Zhou,Field tests of an experimental fully triaxial induction tool, presentedat 2003 SPWLA Annual Logging Symposium, June 22-25, Galveston, Tex.,paper QQ.

Logging-while-drilling (“LWD”) measurements made by well logginginstruments such as one identified by the trademark PERISCOPE, which isa trademark of the assignee of the present disclosure, represent an LWDcounterpart of multi-axial wireline induction instruments. LWDinstruments are typically conveyed through wellbores during drilling orduring “tripping” of drill pipe or other pipe through a wellbore. Theforegoing PERISCOPE LWD instruments are typically used for wellplacement within selected subsurface rock formations or reservoirportions of such formations. However the full potential of thesemulti-axial LWD measurements for quantitative formation evaluation,especially for evaluation of formation resistivity anisotropy at allapparent dip angles, has not heretofore been used.

Interpretation of wireline 3D induction measurements is based on onedimensional parametric inversion. See, e.g., Wang, H., Barber, T.,Rosthal, R., Tabanou, J., Anderson, B., and Habashy, T., Fast andrigorous inversion of triaxial induction logging data to determineformation resistivity anisotropy, bed boundary position, relative dipand azimuth angles, presented at the 2003 SEG Annual Meeting, October27-30, Dallas, Tex. However, there is no such inversion procedureavailable for multi-axial LWD measurements, where ideally theresistivity anisotropy interpretation would be done essentially inreal-time during the drilling of the wellbore.

U.S. Pat. No. 6,998,844, issued to Omeragic et al and assigned to theassignee of the present disclosure, describes making electromagneticpropagation measurements using transverse and tilted magnetic dipoleantennas (“transverse” and “tilted” in the present context means withreference to the longitudinal axis of the well logging instrument). Suchantennas are used in the PERISCOPE instrument described above. The '844patent also describes a method for removing the “invasion” effect(effect of change in resistivity of formations proximate the wellborewall by displacement of native fluid in the pore spaces with liquidphase of the drilling fluid) and shoulder-bed effect (effects of axiallyadjacent formations to the one under evaluation) from the anisotropymeasurement, based on model-based parametric inversion. U.S. Pat. No.6,594,584, issued to Omeragic et al and also assigned to the assignee ofthe present disclosure discloses a distance-to boundary parametricinversion that includes anisotropy inversion from an interval(longitudinally along the wellbore) of electromagnetic measurement data.

There continues to be a need for determination of formation resistivity,resistivity anisotropy and formation bedding attitude (“dip”) fromelectromagnetic measurements made during the drilling of a wellbore.

SUMMARY

A summary of certain embodiments disclosed herein is set forth below. Itshould be understood that these aspects are presented merely to providethe reader with a brief summary of these certain embodiments and thatthese aspects are not intended to limit the scope of this disclosure.Indeed, this disclosure may encompass a variety of aspects that may notbe set forth below.

In accordance with one aspect of the present disclosure a systemincludes an electromagnetic logging tool having transmitter and receiverantennas oriented as a longitudinal magnetic dipole and at least one ofa tilted magnetic dipole or a transverse magnetic dipole, theelectromagnetic logging tool being capable of making dipole sensitiveelectromagnetic measurements within a surface formation. The system alsoincludes a processor capable of: (a) determining formation layerboundaries and horizontal resistivities of the formation layers basedupon longitudinal magnetic dipole measurements obtained using theelectromagnetic logging tool; (b) determining vertical resistivities ofthe formation layers based upon anisotropy sensitive electromagneticmeasurements obtained using the electromagnetic logging tool, (c)inverting the symmetrized and anti-symmetrized electromagneticmeasurements obtained using the electromagnetic logging tool to updatethe vertical resistivities of the formation layers obtained at (b) toobtain improved vertical resistivities of the formation layers and todetermine corresponding dips thereof; (d) inverting the longitudinalmagnetic dipole measurements, the anisotropy sensitive measurements, andthe symmetrized and anti-symmetrized measurements to update the improvedvertical resistivities obtained at (c) to obtain further improvedvertical resistivities, update the layer boundaries obtained at (a) toobtain improved layer boundaries, and update the dips obtained at (c) toobtain improved dips; and (e) inverting the longitudinal magnetic dipolemeasurements, the anisotropy sensitive measurements, and the symmetrizedand anti-symmetrized measurements to update the horizontal resistivitiesobtained at (a) to obtain improved horizontal resistivities, update theimproved layer boundaries obtained at (d) to obtain further improvedlayer boundaries, and update the improved dips obtained at (d) to obtainfurther improved dips.

In accordance with another aspect of the present disclosure, a methodincludes using an electromagnetic logging tool to obtainingnon-directional electromagnetic measurements, anisotropy sensitiveelectromagnetic measurements, and directional electromagneticmeasurements in a subsurface formation. The method further includes: (a)determining an initial formation model using at least one of thenon-directional electromagnetic measurements or the directionalelectromagnetic measurements, the initial formation model defining layerboundaries; (b) using the non-directional electromagnetic measurementsto invert for horizontal resistivities and updating the formation modelbased on the horizontal resistivities; (c) using the anisotropysensitive electromagnetic measurements to invert for verticalresistivities and updating the formation model based on the verticalresistivities; (d) using the directional electromagnetic measurements toinvert for vertical resistivities that are improved in accuracy relativeto the vertical resistivities obtained in (c) and to invert for dipvalues, and updating the formation model based on the improved verticalresistivities and the dip values; (e) using the non-directional,directional, and anisotropy sensitive electromagnetic measurements toinvert for vertical resistivities that are improved in accuracy relativeto the vertical resistivities obtain in (d), to invert for layerboundaries that are improved in accuracy relative to the layerboundaries obtain in (a), and to invert for dip values that are improvedin accuracy relative to the dip values obtained in (d), and updating theformation model based on the improved vertical resistivities, layerboundaries, and dip values; and (f) using the non-directional,directional, and anisotropy sensitive electromagnetic measurements toinvert for horizontal resistivities that are improved in accuracyrelative to the horizontal resistivities obtained in (b), to invert forlayer boundaries that are improved in accuracy relative to the layerboundaries obtained in (e), and to invert for dip values that areimproved in accuracy relative to the dip values obtained in (e), andupdating the formation model based on the improved horizontalresistivities, layer boundaries, and dip values.

In accordance with a further aspect of the present disclosure, amulti-step electromagnetic inversion method includes the steps ofobtaining non-directional, anisotropy, and directional resistivitymeasurements in a formation using an electromagnetic logging tool,identifying bed boundaries of the formation, obtaining a horizontalresistivity profile using the non-directional resistivity measurements,obtaining a vertical resistivity profile using the anisotropyresistivity measurements, improving the vertical resistivity profile andobtaining dip values using the directional resistivity measurements, andinverting for each of vertical resistivity, horizontal resistivity, dipvalues, and bed boundaries using all of the non-directional, anisotropy,and directional resistivity measurements to obtain a formation model.

Various refinements of the features noted above may exist in relation tovarious aspects of the present disclosure. Further features may also beincorporated in these various aspects as well. These refinements andadditional features may exist individually or in any combination. Forinstance, various features discussed below in relation to one or more ofthe illustrated embodiments may be incorporated into any of theabove-described aspects of the present disclosure alone or in anycombination. Again, the brief summary presented above is intended onlyto familiarize the reader with certain aspects and contexts ofembodiments of the present disclosure without limitation to the claimedsubject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of this disclosure may be better understood upon readingthe following detailed description and upon reference to the drawings inwhich:

FIG. 1 is a schematic diagram of a subterranean well logging system thatincludes a logging-while-drilling instrument capable of makingmeasurements in accordance with an embodiment of the present disclosure;

FIG. 1B shows geologic structure of a 1-D formation model in accordancewith aspects of the present disclosure;

FIG. 1C shows resistivities of the 1-D model of FIG. 1A in accordancewith aspects of the present disclosure;

FIG. 2 shows a log(R) response in accordance with aspects of the presentdisclosure;

FIG. 3 shows the initial formation model compared with the true model inaccordance with aspects of the present disclosure;

FIG. 4 shows the inversion results, inverted for Rh only, in accordancewith aspects of the present disclosure;

FIG. 5 shows inversion results, inverted for Rv only, in accordance withaspects of the present disclosure;

FIG. 6 shows inversion results, inverted for Rv and dip, in accordancewith aspects of the present disclosure;

FIG. 7 shows confidence level calculations in accordance with aspects ofthe present disclosure;

FIG. 8 shows inversion quality control graphs in accordance with aspectsof the present disclosure;

FIGS. 9A through 9D show comparison of tool responses, with and withoutborehole effect in accordance with aspects of the present disclosure;

FIG. 10 shows inversion results in accordance with aspects of thepresent disclosure; and

FIG. 11 shows inversion results with reduced borehole effect inaccordance with aspects of the present disclosure.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

One or more specific embodiments of the present disclosure are describedbelow. These embodiments are only examples of the presently disclosedtechniques. Additionally, in an effort to provide a concise descriptionof these embodiments, all features of an actual implementation may notbe described in the specification. It should be appreciated that in thedevelopment of any such implementation, as in any engineering or designproject, numerous implementation-specific decisions are made to achievethe developers' specific goals, such as compliance with system-relatedand business-related constraints, which may vary from one implementationto another. Moreover, it should be appreciated that such developmentefforts might be complex and time consuming, but would nevertheless be aroutine undertaking of design, fabrication, and manufacture for those ofordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the presentdisclosure, the articles “a,” “an,” and “the” are intended to mean thatthere are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements. Theembodiments discussed below are intended to be examples that areillustrative in nature and should not be construed to mean that thespecific embodiments described herein are necessarily preferential innature. Additionally, it should be understood that references to “oneembodiment” or “an embodiment” within the present disclosure are not tobe interpreted as excluding the existence of additional embodiments thatalso incorporate the recited features.

FIG. 1A illustrates a drilling rig and drill string in which themeasurements used with methods of the present disclosure can be made. Aland-based platform and derrick assembly 10 are positioned over awellbore 11 drilled through subsurface formations F. In the illustratedexample, the wellbore 11 is formed by rotary drilling in a manner thatis known in the art. Those skilled in the art will appreciate, however,that the present disclosure also finds application in directionaldrilling applications using hydraulically operated drill motors as wellas rotary drilling. Furthermore, it is understood that the techniquesset forth in this disclosure is no way limited to use on land-basedrigs.

A drill string 12 is suspended within the wellbore 11 and includes adrill bit 15 at its lower end. The drill string 12 is rotated by arotary table 16, energized by means not shown, which engages a kelly 17at the upper end of the drill string. The drill string 12 is suspendedfrom a hook 18, attached to a traveling block (also not shown), throughthe kelly 17 and a rotary swivel 19 which permits rotation of the drillstring relative to the hook.

Drilling fluid or mud 26 is stored in a pit 27 formed at the well site.A pump 29 delivers the drilling fluid 26 to the interior of the drillstring 12 via a port in the swivel 19, inducing the drilling fluid toflow downwardly through the drill string 12 as indicated by thedirectional arrow 9. The drilling fluid exits the drill string 12 viaports in the drill bit 15, and then circulates upwardly through theregion between the outside of the drill string and the wall of thewellbore, called the annulus, as indicated by the direction arrows 32.In this manner, the drilling fluid lubricates the drill bit 15 andcarries formation cuttings up to the surface as it is returned to thepit 27 for recirculation.

The drill string 12 further includes a bottom hole assembly, generallyshown at 34 near the drill bit 15 (typically within several drill collarlengths from the drill bit). The bottom hole assembly 34 may includecapabilities for measuring, processing, and storing information, as wellas communicating with the surface. The bottom hole assembly (“BHA”) 34thus includes, among other things, a measuring and local communicationsapparatus 36 for determining and communicating the resistivity of theformation F surrounding the wellbore 11. The communications apparatus36, which includes an azimuthally sensitive resistivity measuringinstrument, includes a first pair of transmitting/receiving antennas T,R, as well as a second pair of transmitting/receiving antennas T″, R″.The second pair of antennas T″, R″ is symmetric with respect to thefirst pair of antennas T, R. The resistivity instrument 36 furtherincludes a controller to control the acquisition of data, as is known inthe art. The resistivity instrument may be one described more fully inU.S. Pat. No. 7,382,135 issued to Li et al. and assigned to the assigneeof the present application. The foregoing instrument is used under thetrademarks PERISCOPE 15 and PERISCOPE 100, which are trademarks of theassignee of the present application. The PERISCOPE instruments havetilted dipole antennas. Types of interpretation of measurements fromsuch tilted dipole antennas is described more fully in the Omeragic etal. '584 patent referred to above. For purposes of making measurementsusable with methods according to the present disclosure, it is onlynecessary to have any combination of electromagnetic antennas withdipole moments oriented to be sensitive: (i) primarily to “horizontalresistivity” (Rh), which is electrical resistivity of a rock formationmeasured parallel to the attitude of the formation layer (“beddingplane”); (ii) primarily to “vertical resistivity” (Rv) or resistivityanisotropy, which is electrical resistivity measured perpendicularly tothe bedding plane, and (iii) be able to make or synthesize “symmetric”and “anti-symmetric” cross dipole measurements (such measurements aresensitive to the direction and magnitude of formation dip or beddingplane attitude with respect to the wellbore/instrument longitudinalaxis).

The BHA 34 further includes instruments housed within drill collars 38,39 for performing various other measurement functions, such asmeasurement of the natural radiation, density (gamma ray or neutron),and pore pressure of the formation F. At least some of the drill collarsare equipped with stabilizers 37, as are well known in the art.

A surface/local communications subassembly 40 is also included in theBHA 34, just above the drill collar 39. The subassembly 40 includes atoroidal antenna 42 used for local communication with the resistivitytool 36 (although other known local-communication means may be employedto advantage), and a known type of acoustic telemetry system thatcommunicates with a similar system (not shown) at the earth's surfacevia signals carried in the drilling fluid or mud. Thus, the telemetrysystem in the subassembly 40 includes an acoustic transmitter thatgenerates an acoustic signal in the drilling fluid (a.k.a., “mud-pulse”)that is representative of measured downhole parameters. Such telemetry,and related telemetry techniques that impart acoustic signals in thedrilling fluid may be generally characterized as modulating the flow offluid in the drill string or pipe string.

The generated acoustical signal is received at the surface bytransducers represented by reference numeral 31. The transducers, forexample, piezoelectric transducers, convert the received acousticalsignals to electronic signals. The output of the transducers 31 iscoupled to an uphole receiving subsystem 90, which demodulates thetransmitted signals. The output of the receiving subsystem 90 is thencoupled to a computer processor 85 and a recorder 45. The processor 85may be used to determine the formation resistivity profile (among otherthings) on a “real time” basis while logging or subsequently byaccessing the recorded data from the recorder 45. The computer processoris coupled to a monitor 92 that employs a graphical user interface(“GUI”) through which the measured downhole parameters and particularresults derived therefrom (e.g., resistivity profiles) are graphicallypresented to a user.

An uphole transmitting system 95 is also provided for receiving inputcommands from the user (e.g., via the GUI in monitor 92), and isoperative to selectively interrupt the operation of the pump 29 in amanner that is detectable by transducers 99 in the subassembly 40. Inthis manner, there is two-way communication between the subassembly 40and the uphole equipment. A suitable subassembly 40 is described ingreater detail in U.S. Pat. Nos. 5,235,285 and 5,517,464, both of whichare assigned to the assignee of the present application. Those skilledin the art will appreciate that alternative acoustic techniques, as wellas other telemetry means (e.g., electromechanical, electromagnetic), canbe employed for communication with the surface.

In one example of such alternative signal telemetry, the drill string 12may be substituted by a “wired” pipe string, which includes a wiredsignal telemetry channel forming part of each pipe segment, and anelectromagnetic coupler disposed on a thread shoulder at eachlongitudinal end of each pipe segment. See, for example, U.S. Pat. No.7,040,415 issued to Boyle et al. and assigned to the assignee of thepresent application, the entirety of which is incorporated herein byreference. Referring to FIG. 1A of U.S. Pat. No. 7,040,415, an exampleof such telemetry system may include the following. The drill string 6that employs a telemetry system 100 in accordance with the presentexample includes multiple interconnected tubular members (describedfurther below) suspended from a derrick and platform assembly 10 by wayof a traveling block (not shown) and a hook 18. The upper end of thedrill string 6 is defined by a kelly joint 17, the uppermost tubularmember in the string, which is engaged by a conventional torque-applyingmeans including a rotary table 16 for rotating the kelly joint as wellas the entire drill string 6. A swivel 19 connects the hook 18 to thekelly joint 17, and permits rotation of the kelly joint and the drillstring 6 relative to the hook.

Still referring to FIG. 1A of U.S. Pat. No. 7,040,415, the lower end ofthe drill string 6 may include a drill bit 15 which drills through theformation F to create the wellbore 7 as explained above. The drill bitis connected for rotation with the drill string 6 in a rotary drillingconfiguration of the sort described above.

The drill string 6 as explained above may otherwise employ a “top-drive”configuration wherein a power swivel rotates the drill string instead ofa kelly joint and rotary table. Those skilled in the art will alsoappreciate that “sliding” drilling operations may otherwise be conductedwith the use of a well-known Moineau-type mud motor that convertshydraulic energy from the drilling mud pumped from a mud pit downthrough the drill string 106 into torque for rotating a drill bit.Drilling may furthermore be conducted with so-called “rotary-steerable”systems which are known in the related art. The various aspects of thepresent disclosure are adapted to each of these configurations and arenot limited to conventional rotary drilling operations, although suchequipment and methods will be described herein for illustrativepurposes. The drill string telemetry system 100 can include a cabledcommunication link 5 b having at least two spaced apart adapter subs(e.g., 9 a, 9 b, 9 c) within the drill string 6 and a cable 112 (seeFIGS. 1B and 1C of U.S. Pat. No. 7,040,415) connecting the two adaptersubs 9 a, 9 b for communication of a signal therebetween. The cabledcommunication link 5 b can include a communicative coupler permittingthe adapter subs to also serve as a component in a piped communicationlink 5 a.

Referring collectively to FIG. 1A of U.S. Pat. No. 7,040,415 and FIG. 1Aof the present application, measurements from the well logginginstrument 34 may be communicated to the surface unit 2 (including arecording unit 45) over the signal channel in the drill string 6 using acable 3 connected to the swivel 19. The foregoing example, just as theexample explained with reference to FIG. 1A of the present application,is only intended to illustrate the principle of communication betweenthe BHA 36 (including the well logging instrument 34 shown in FIG. 1)and the recording unit 45 and is not intended to limit the scope oftelemetry devices that may be used in accordance with the presentdisclosure.

In methods according to the present disclosure, measurements made frominstruments such as those described above are processed to determinehorizontal resistivity (apparent resistivity measured transversely tothe thickness of a formation layer), vertical resistivity (resistivitymeasured along the direction of the thickness of a formation layer) anddip (attitude of the layers with respect to a selected axial reference).

The 1-D parametric inversion used to interpret wireline triaxialinduction measurements is based on a “layer-cake” (substantially planar,parallel bedded formations) transversely isotropic (TI) formation model.Using a similar basis for layered rock formation models, and usingmeasurements made by instruments such as the ones described above withreference to FIG. 1A, an inversion procedure according to embodiments ofthe present disclosure may determine horizontal and verticalresistivity, Rh and Rv, respectively, formation dip (direction andmagnitude) and thicknesses of all formation layers traversed by the welllogging instrument. Methods according to the present disclosure takeadvantage of the fact that different measurements made by the instrumentare predominantly sensitive to different formation model parameters. Amulti-step inversion procedure according to the present disclosuretypically includes the following general steps, which will beindividually explained further below.

(1) Determine initial axial positions of formation layer (“bed”)boundaries from conventional resistivity (that is, resistivity measuredusing longitudinal magnetic dipole antennas or galvanic devices) ordirectional responses from measurements made by instruments such as thePERISCOPE instrument described above.

(2) From conventional (e.g., longitudinal magnetic dipole, sometimesalso called “non-directional” measurements) resistivity measurements,invert for horizontal resistivity Rh. In this step it is assumed thatthe formation is isotropic, i.e., Rv=Rh, and the layer (bed) thicknessesand dip are known.

(3) Invert for vertical resistivity (Rv) using “anisotropy”measurements. Such anisotropy measurements may be transverse or tiltedmagnetic dipole measurements.

(4) Invert for Rv and dip using symmetrized and anti-symmetrizedmeasurements. As explained above, such measurements may be made fromcertain triaxial induction cross-dipole measurements or may besynthesized from the tilted dipole measurements made using the PERISCOPEinstrument described above.

(5) Invert for Rv, dip and bed thicknesses (or bed boundary locations)using all available measurements.

(6) Invert for Rh, Dip and bed thicknesses (or bed boundary locations)using all available measurements.

(7) Examine the misfit between the measurement and the modeled responsein step (6). If needed, perturb the solution to the inversion of step(6) to generate a new inversion model, and then repeat steps (5) and(6). Repeat steps (7), (5) and (6) until the misfit (in step 7) fallsbelow a selected threshold. The result at that time will be the finalmodel of the formations.

It will be noted that each of the above general steps (1) through (6) isitself an inversion procedure. The results of each individual inversionstep (1) through (6) may be used as the initial model for eachsubsequent inversion step in the above procedure.

FIG. 1B shows a 1-D formation model having dipping formations, shown at102-118. The synthetic response of a well logging instrument disposed ina simulated vertical well 100 penetrating such formations 102-118 wasgenerated, and the synthetic response was used to perform an inversion,the results of which are shown in FIG. 7. As will be readily appreciatedby those skilled in the art, “dip” calculated using methods according tothe present disclosure represents the attitude of the formation layerswith respect to the axis of the wellbore and/or well logging instrument.In cases where the wellbore is in fact geodetically vertical, thedetermined dip will represent the geodetic dip. In cases where thewellbore trajectory is not vertical, the determined dip may be convertedto geodetic dip by adjusting for the wellbore geodetic trajectory. Suchtrajectory is typically measured substantially along the entire wellboreusing directional sensors (e.g., a combination of triaxial magnetometerand triaxial accelerometer). The steps set forth above in an examplemethod according to the present disclosure will be explained in moredetail below.

1. Obtaining the Initial Estimate of Bed Boundary Positions fromResistivity Responses

General procedures for estimating initial formation layer (“bed”)boundary positions from resistivity measurements include selecting aresistivity response (R). In one example, the response R may be obtainedusing the PERISCOPE instrument described above or any longitudinalmagnetic dipole electromagnetic instrument and selecting one of theresistivity response curves, for example, phase shift. The logarithmthereof, log(R), is then calculated. Then, the derivative of log(R) withrespect to axial position (measured depth) may be calculated. The peakson the derivative curve may be selected as the bed boundaries.

Next, bed thicknesses are examined. If the thinnest bed is below apredefined cutoff or threshold value, then the following procedures maybe used. If one of the adjacent beds is thick (e.g., above the thresholdthickness), the selected bed boundary may be moved toward the thick bedto increase the thickness of the layer having below the thresholdthickness (the “thin bed”). If both adjacent layers are thick, the bedboundary may be moved toward the bed having lower resistivity contrastwith respect to the thin bed. If both adjacent beds are thin (below thethreshold thickness), remove the bed boundary with lower resistivitycontrast with reference to the thin bed under examination. The foregoingprocess may be repeated until all the thin beds are removed from theinitial estimate. If some of the layers are too thick (i.e. >3 meters),additional bed boundaries may be added as may be appropriate.

Once the bed boundaries are defined, the resistivity of a selectedresponse (e.g., the phase response identified above) is determined atthe axial middle of the beds. For each bed, such value is the initialestimated value of horizontal resistivity, Rh. An assumption may then bemade about the formation dip using external information, e.g., imagemeasurements. If no such external information is available, zero dip canbe chosen as the initial estimate.

FIG. 2 shows the log(R) response of a 28 inch spacing phase response atcurve 120 and the selected bed boundaries at 124 using the foregoingprocedure. The derivative of log(R) is shown at 122 The foregoingprocedure identifies all the actual bed boundaries, but it may alsoidentify false boundaries. The estimates of bed boundary axial positionsare close to the actual model positions.

FIG. 3 shows the initial formation estimate derived as explained abovewith reference to FIG. 2 and FIG. 3 compared with the actual formationmodel used. Rh, Rv and Dip values are plotted along MD (“measured depth”or axial position along the length of the wellbore). Model input valuesof Rh are shown at curve 126, model input Rv values are shown at curve128, initial Rh and Rv are shown at curves 127 and 130, respectively.Model dip is shown in the second track of the log presentation at curve132 and initial dip is shown at curve 134. Discontinuities in Rh and Rvtypically indicate positions of bed boundaries. The initial estimate ofRh appears very close to the actual model value thereof. Rv and dipvalues, however are quite different between the initial estimatedetermined using the above procedure and the actual model.

In order to evaluate the difference between the initial estimate and theactual model, the following formula is proposed to describe the relativeaccuracy (in percent), also shown in FIG. 3 as the curve in the righthand “track.” The global factor is used to define accuracy of theinverted model accuracy in this note. The global accuracy factor isdefined as weighted average of Rh, Rv and dip accuracy:

${Accuracy} = {{100\%} - {w_{Rh}{\min\left( {\frac{{\log\; 10\left( {R_{Hmodel}/R_{Htrue}} \right)}}{Rh\_ cutoff},1} \right)}} - {w_{{Rv}\;}{\min\left( {\frac{{\log\; 10\left( {R_{Vmodel}/R_{Vtrue}} \right)}}{Rv\_ cutoff},1} \right)}} - {w_{dip}{\min\left( {\frac{{{dip}_{model} - {dip}_{true}}}{dip\_ cutoff},1} \right)}}}$

The weighting and cutoff values are determined according to theimportance and tolerance error of each parameter. Convenient values are:w _(Rh) =w _(Rv) =w _(dip)=⅓Rh_cutoff=log 10(1.1)Rv_cutoff=log 10(1.5)dip_cutoff=5

The above outlined methodology does not include anisotropy anddirectional measurements, and has a limitation in that if Rh is notchanging, it will not identify Rv discontinuities. Anisotropy anddirectional measurements (e.g., appropriate measurement channels fromthe PERISCOPE instrument) can be used in such cases because layerboundaries can be identified from peaks in responses that correspond toboundary crossing by a tilted or transverse magnetic dipole antenna. Foroptimal implementation to symmetrized directional measurements, depthshifting can be applied and performed on individual pairs ofmeasurements

2. Invert Rh from Longitudinal Magnetic Dipole Measurements

Conventional resistivity (e.g., longitudinal magnetic dipole)measurements may be used to invert for horizontal resistivities, becausethe response of such instruments in are primarily sensitive tohorizontal resistivity, Rh, in vertical and low deviation wells (i.e.,when the instrument axis is roughly perpendicular to the layers of theformation). Isotropic resistivity (Rh=Rv) can be assumed, and bedthicknesses and formation dip can be fixed. FIG. 4 shows the invertedresults, using the same curve numbering notation as in FIG. 3. The Rhvalue has improved slightly, because the initial estimate was alreadyvery close to the actual model value. Rv and dip values are not updatedin this step.

3. Invert Rv from Anisotropy Channels

In vertical or low angle wells (or combinations of well inclination andformation dip that result in the well being substantially normal to theformation layering), anisotropy responses (e.g., tilted or transversemagnetic dipole antenna measurements) are the most sensitive to Rv. Inthis step they are used to invert for Rv only, fixing Rh, dip andpositions of the bed boundaries from the previous step. The invertedresults are shown in FIG. 5, using the same curve numbering notation asfor FIGS. 3 and 4. A significant improvement in Rv values and globalmodel accuracy can be observed.

4. Invert Rv and Dip from Directional Channels

At non zero dip, directional (both symmetrized and anti-symmetrized)measurements are also sensitive to formation dip and verticalresistivities (Rv). See, for example, U.S. Pat. No. 7,536,261 issued toOmeragic et al. and assigned to the assignee of the present application.Therefore, these responses may be used to update Rv and dip, with Rh andpositions of the bed boundaries being fixed. The results for a testexample are shown in FIG. 6, using the same curve numbering notation asin FIGS. 3-5. The dip angle is observed to be very close to the modeledvalue. Rv is also slightly improved. The improvement in inversion outputresult is also reflected in the global accuracy curve.

5. Invert Rv, Dip and Bed Boundaries from all Measurements;

6. Invert Rh, Dip and Bed Boundaries from all Measurements;

7. Perturbing the Model and Restarting as Required.

After the first 4 steps are performed as explained above, the estimatesof formation Rh, Rv and dip are typically already close to a finalsolution, and the present steps, 5 through 7, represent a “fine tuning”It is computationally the most expensive, but typically the steprequires only a small number of iterations to reach convergence orminimization of a cost function.

For the test example, the results are shown in FIG. 7. The originalmodel is reconstructed fully, so restarting the inversion after modelperturbation (step 7) was not necessary. In certain cases the inversionmay become “trapped” at a local minimum in the cost function. In suchcases the inversion can be resumed by perturbing the final modelobtained when the cost function is minimized.

Log Quality Control

Although most of the inversion techniques provide an estimate of thesensitivity of the inverted parameters to the measurement input, areliable characterization of the uncertainty and proper log qualitycontrol is not straightforward. Therefore, no matter how well aninversion procedure is developed, knowing how much to rely on theinversion output is critical for decision making Typically thereconstruction of the measurement by the selected model is taken as thebasic indicator of how well the inversion(s) has/have converged to asolution. However, in some cases such an approach may not be sufficient,especially when inversion solutions are not unique. Therefore, thepresent disclosure also provides a method which takes different keyelements from to define log quality controls to enable the user toevaluate the reliability of the inversion results.

Elements for Constructing Quality Control (QC) Indicators

Three categories of elements may be considered for the purpose ofconstructing QC indicators, in certain exemplary embodiments: (a) modelvalidity, (b) data fit, and (c) uncertainty of inversion parameters.Each of these is described in more detail below.

(a) Model validity (non-1D factor) is a factor describing how well thesolution approximations match the actual formation properties. Usuallycertain approximations are made in the forward model for the purpose ofsimplicity. In this specific case, it is assumed that the formation is alayered medium. The final result is only reliable when such 1-Dapproximation is valid for the formations being evaluated.

Two exemplary factors that can be used to compute the non-1D factor arestandard deviation in estimated formation dip and variation of formationazimuth angle. As to standard deviation, as previously stated, the 1-Dmodel assumes constant formation dip within the processing window. Dipstandard deviation within the processing window is a good indicator ofthe degree of deviation from the 1-D approximation. The dip value can beobtained from other measurements, or may be obtained by any results fromthe PERISCOPE instrument measurement inversion. The standard deviationof dip is calculated as:

${dip\_ std} = \sqrt{\frac{1}{N}{\sum\limits_{i = {{- N}/2}}^{N/2}\left( {{dip}_{i} - {dip}_{mean}} \right)^{2}}}$

wherein N is the number of measurement points within the processingwindow.

${dip}_{mean} = {\frac{1}{N}{\sum\limits_{i = {{- N}/2}}^{N/2}{dip}_{i}}}$is the mean value of dip within the processing window.

A LQC indicator may be defined based on the dip standard deviationwithin the processing window.

${LQC}_{dip\_ std} = {1 - {\min\left( {\frac{dip\_ std}{{cutoff\_ dip}{\_ std}},1} \right)}^{{power\_ dip}{\_ std}}}$

cutoff_dip_std and power_dip_std are scaling factors determined fromtesting data.

As to the variation of formation azimuth angle, the apparent azimuthangle in a “top of hole” coordinate system is given by the PERISCOPEinstrument measurement channel (known as DANG angle).

Similar to that defined for dip, a QC indicator related to standarddeviation of DANG angle can be defined as:

${LQC}_{DANG\_ std} = {1 - {\min\left( {\frac{DANG\_ std}{{cutoff\_ DANG}{\_ std}},1} \right)}^{{power\_ DANG}{\_ std}}}$

Where DANG_std is the standard deviation of DANG values within theprocessing window.

cutoff_DANG_std and power_DANG_std are scaling factors

(b) Data fit: Data fit is a factor describing how well the modelpredicted instrument responses match with the actual instrumentmeasurements made in the rock formations. Several types of data fittingfactors have been considered.

Inversion Residual.

Inversion residual is the cost function which the inversion is intendedto minimize. The cost function is essentially a combination of datamisfit for measurement used in the inversion and the regularizationterms. The formulation of the cost function may be:

$C = \sqrt{\frac{{\sum\limits_{j = 1}^{n_{pos}}{\sum\limits_{i = 1}^{n_{channels}}{w_{i}^{2}\left( {H_{d,i} - H_{m,i}} \right)}^{2}}} + {{regularization}\mspace{14mu}{terms}}}{n_{channels} \times n_{pos}}}$

where n_(pos) is the number of measurement positions within theinversion processing window, and n_(channels) is the number ofmeasurement channels (number of individual measurements used in theinversion at each position).

Weighted Data Fitting Errors for all or Part of the MeasurementChannels.

Fitting errors for part or all of the available ARC or PERISCOPEinstrument measurements may be defined as:

Relative Error:

${misfit\_ ARC} = \frac{\sum\limits_{i \in {ARC}}^{\;}\;{w_{i}^{2}\left( {H_{d,i} - H_{m,i}} \right)}^{2}}{\sum\limits_{i \in {ARC}}^{\;}\;{\max\left( {{w_{i}^{2}\left( H_{d,i} \right)}^{2},1} \right)}}$

Absolute Error:

${cost\_ ARC} = \sqrt{\frac{\sum\limits_{i \in {ARC}}^{\;}\;{w_{i}^{2}\left( {H_{d,i} - H_{m,i}} \right)}^{2}}{n_{ARC}}}$

Fitting errors for all or part of Symmetrized directional (D),anti-symmetrized directional (X) and anisotropy measurement channels(A):

Relative Error:

${misfit\_ DXA} = \frac{{\sum\limits_{i \in {DXA}}^{\;}{w_{i}^{2}\left( {H_{d,i} - H_{m,i}} \right)}^{2}}\;}{\sum\limits_{i \in {DXA}}^{\;}{\max\left( {{w_{i}^{2}\left( H_{d,i} \right)}^{2},1} \right)}}$

Absolute Error:

${cost\_ DXA} = \sqrt{\frac{\sum\limits_{i \in {DXA}}^{\;}{w_{i}^{2}\left( {H_{d,i} - H_{m,i}} \right)}^{2}}{n_{DXA}}}$

(c) Uncertainty of the inversion parameters: Uncertainty is a factorreflecting data sensitivity to the inverted parameters. Uncertainty ofthe inversion results due to noise in the measurement data is determinedby the data sensitivity to the model parameters, as well as theinversion procedures. Direct Monte Carlo simulation is one technique forestimating inversion uncertainty and is performed by perturbing themeasurements with a known noise level and performing the inversion withthe perturbed measurements. After running sufficient number ofrealizations of the inversion, the inversion results can be analyzedstatistically. The standard deviation of the inversion results can beused to define the inversion uncertainty. It is usually not practical torun a large number of inversions due to the speed requirement,especially for real time application. In this case a fast approximateapproach is used to estimate from deterministic inversion using themodel covariance matrix. See Habashy, T., Abubakar, A., 2004, “A generalframework for constraint minimization for the inversion ofelectromagnetic measurements,” Progress in Electromagnetics Research(PIER), 46, pp. 265-312.

Constructing QC Using Basic QC Elements:

The 3 categories of QC elements described above may be combined todefine inversion quality for Rh, Rv, Dip, Azimuth as well as the globalquality.

Quality of Rh:

Combining Rh uncertainty R_(h) _(—) _(unc), inversion residual χ, datafitting for ARC (or PERISCOPE) misfit_ARC and cost_ARC

Formulation from Misfit (“Relative Error”):

${LQC}_{{Rh}\; 1} = \left( {1 - {\min\left( {\frac{R_{h\_ unc} \times C \times {misfit\_ ARC}}{R_{h} \times {cutoff}_{{Rh\_ unc}{\_ misfit}}},1} \right)}^{{power\_ misfit}{\_ ARC}}} \right)$

Formulation from Absolute Error (in High Resistivity Situation):

${LQC}_{{Rh}\; 2} = \left( {1 - {\min\left( {\frac{\min\;\left( {{R_{h\_ unc} \times C},10} \right) \times {cost\_ ARC}}{R_{h} \times {cutoff}_{{Rh\_ unc}{\_ cost}}},1} \right)}^{{power\_ misfit}{\_ ARC}}} \right)$

The Final Rh QualityLQC _(Rh)=max(LQC _(Rb1) ,LQC _(Rb2))

Quality of Rv:

Combining Rv uncertainty R_(V) _(—) _(unc) inversion residual χ, datafitting for directional and anisotropy channels (misfit_DXA andcost_DXA).

Formulation from Relative Errors:

${LQC}_{{Rv}\; 1} = {\left( {1 - {\min\left( {\frac{R_{v\_ unc} \times C \times {misfit\_ DXA}}{R_{v} \times {cutoff}_{{Rv\_ unc}{\_ misfit}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right){LQC}_{dip\_ std}}$

Formulation from Absolute Errors:

${LQC}_{{Rv}\; 2} = {\left( {1 - {\min\left( {\frac{\min\;\left( {{R_{v\_ unc} \times C},10} \right) \times {cost\_ DXA}}{R_{v} \times {cutoff}_{{Rv\_ unc}{\_ cost}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right){LQC}_{dip\_ std}}$

Final Rv Quality:LQC _(Rv)=max(LQC _(Rv1) ,LQC _(Rv2))

LQC for True Dip:

Combining dip uncertainty dip_(true) _(—) _(unc) inversion residual C,data fitting for directional and anisotropy channels (misfit_DXA andcost_DXA)

Formulation from Relative Error:

${LQC}_{{true\_ dip}\; 1} = \left( {1 - {\min\left( {\frac{{dip}_{true\_ unc} \times C \times {misfit\_ DXA}}{{cutoff}_{{true\_ dip}{\_ unc}{\_ misfit}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right)$

Formulation from Absolute Error:

${LQC}_{{true\_ dip}\; 2} = \left( {1 - {\min\left( {\frac{{dip}_{true\_ unc} \times C \times {cost\_ DXA}}{{cutoff}_{{true\_ dip}{\_ unc}{\_ cost}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right)$

Final Dip Quality:

${LQC}_{true\_ dip} = \left\{ \begin{matrix}{{\max\left( {{LQC}_{{true\_ dip}\; 1},{LQC}_{{{true\_ di}p}\; 2}} \right)}{LQC}_{dip\_ std}} & {{dip}_{app} < {2{^\circ}}} \\{{\max\left( {{LQC}_{{true\_ dip}1},{LQC}_{{true\_ dip}2}} \right)}{LQC}_{dip\_ std}{LQC}_{DANG\_ std}} & {else}\end{matrix} \right.$DANG angle variation effect should be removed in vertical cases.

LQC for True Dip Azimuth:

Combining azimuth uncertainty azi_(true) _(—) _(unc), inversion residualC, data fitting for directional and anisotropy channels (misfit_DXA andcost_DXA).

Formulation from Relative Error:

${LQC}_{{true\_ azi}\; 1} = \left( {1 - {\min\left( {\frac{{azi}_{true\_ unc} \times C \times {misfit\_ DXA}}{{cutoff}_{{true\_ azi}{\_ unc}{\_ misfit}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right)$

Formulation from Absolute Error:

${LQC}_{{true\_ azi}\; 2} = {\left( {1 - {\min\left( {\frac{{azi}_{true\_ unc} \times C \times {cost\_ DXA}}{{cutoff}_{{true\_ azi}{\_ unc}{\_ cost}}},1} \right)}^{{power\_ misfit}{\_ DXA}}} \right){LQC}_{dip\_ std}{LQC}_{DANG\_ std}}$

Final Formulation:

${LQC}_{true\_ azi} = \left\{ \begin{matrix}{{\max\left( {{LQC}_{{true\_ azi}\; 1},{LQC}_{{true\_ azi}\; 2}} \right)}{LQC}_{dip\_ std}} & {{{if}\mspace{14mu}{dip}_{app}} < {2{^\circ}}} \\{{\max\left( {{LQC}_{{true\_ azi}1},{LQC}_{{true\_ azi}2}} \right)}{LQC}_{dip\_ std}{LQC}_{DANG\_ std}} & {else}\end{matrix} \right.$Global confidence level is a combination Rh, Rv, Dip and azimuthconfidences.LQC _(global)=(w _(rh) LQC _(Rh) +w _(rv) LQC _(Rv) +w _(dip) LQC_(true) _(—) _(dip) +w _(azi) LQC _(true) _(—) _(azi))/(w _(rh) +w _(rv)+w _(dip) +w _(azi))w _(rh) =w _(rv) =w _(dip) =w _(azi)=1 in general.w _(dip) =w _(azi)=0 if max(R _(h) ,R _(V))/min(R _(h) ,R _(V))≦1.1

Dip and azimuth effect may be discounted in cases of isotropic andhomogeneous rock formations.

All scaling factors and weighting factors are obtained based on both theinversion of realistic synthetic models (with electronics andenvironmental noise included) and inversion of field data.

The resulting qualities may all be ranged from 0 to 1. The values may beconverted into a color map in which the color gradually changes from redto green as the quality values increases from 0 to 1. In general greenindicates good quality and red color will initiate an alert to thesystem operator. Any other type of display may be used to indicate thequality as well as color, such as a curve scaled between zero and unityand displayed with respect to depth.

${Confidence} = {{100\%} - {w_{seg}\frac{seg\_ mismatch}{seg\_ cutoff}} + {w_{pbp}\frac{pbp\_ mismatch}{pbp\_ cutoff}} + {w_{AT}\frac{{AT\_ error}{\_ max}}{AT\_ cutoff}} + {w_{PS}\frac{{PS\_ error}{\_ max}}{PS\_ cutoff}} + {w_{dip}\frac{dip\_ std}{{dip\_ std}{\_ cutoff}}}}$$\mspace{20mu}{{w_{seg} = {w_{pbp} = \frac{1}{3.1}}},\mspace{20mu}{w_{AT} = {w_{PS} = \frac{0.3}{3.1}}},\mspace{20mu}{w_{dip} = \frac{0.5}{3.1}}}$  seg_cutoff = pbp_cutoff = 10%,  AT_cutoff = 0.5  dB,  PS_cutoff = 10^(∘),  dip_std_cutoff = 5^(∘)

FIG. 8 shows a field data example. The first three tracks show theinverted formation model parameters Rh, Rv, Dip, Azimuth. The last trackshows the QC (quality control) for Rh, Rv, Dip, azimuth and the overallinversion quality. At some depths the inversion encountered somedifficulties. At such depths the Rh and Rv curves showed some spikes andthe quality was relatively low. For some regions (i.e. between 7200 to7400 ft) the inverted dip and azimuth showed some reduced QC (indicatedby yellow on the color map, or reductions in the Global Confidence colormap 136 for example) but the determined Rh and Rv are still veryreliable. The Global Confidence may be presented in the form of a coloror gray scale map or a curve at the discretion of the system designer oruser.

Dealing with Borehole Effect

In the forward model the borehole effect is typically ignored forsimplicity. In some cases the borehole effect may be significant andneglecting the borehole effect may lead to inaccurate inversion results.One technique for managing borehole effect is to exclude themeasurements that have large borehole effect, and perform the inversionwith measurements that have more limited borehole effect (typicallythose having larger transmitter to receiver spacing), or conversely,excluding from the inversion procedure those responses from relativelyshort spaced transmitter/receiver combinations.

FIGS. 9A through 9D show a synthetic example, comparing tool responseswith and without large borehole effect. In this case borehole effect issmall for most channels except for the curves marked DPS964 and APS594,which are reflect response of relatively short spacedtransmitter-receiver combinations. FIG. 10 shows the inversion resultswhen curves DPS964 and APS594 are included. The inverted Rv issubstantially different from the Rv model value. In order to reduce theborehole effect on inversion, response curves DPS964 and APS594 wereexcluded from the inversion, and the new results are shown in FIG. 11.The inversion results are much closer to the model values.

Methods according to the present disclosure may provide faster inversionresults than methods used for wireline triaxial induction, thus makingpossible calculation of inversion results substantially in real timeduring drilling a wellbore, if so desired.

While the specific embodiments described above have been shown by way ofexample, it will be appreciated that many modifications and otherembodiments will come to the mind of one skilled in the art having thebenefit of the teachings presented in the foregoing description and theassociated drawings. Accordingly, it is understood that variousmodifications and embodiments are intended to be included within thescope of the appended claims.

What is claimed is:
 1. A system comprising: an electromagnetic loggingtool having transmitter and receiver antennas oriented as a longitudinalmagnetic dipole and at least one of a tilted magnetic dipole or atransverse magnetic dipole, wherein the electromagnetic logging tool iscapable of making dipole sensitive electromagnetic measurements within asurface formation; and a processor capable of: (a) determining formationlayer boundaries and horizontal resistivities of the formation layersbased upon longitudinal magnetic dipole measurements obtained using theelectromagnetic logging tool; (b) determining vertical resistivities ofthe formation layers based upon anisotropy sensitive electromagneticmeasurements obtained using the electromagnetic logging tool; (c)inverting the symmetrized and anti-symmetrized electromagneticmeasurements obtained using the electromagnetic logging tool to updatethe vertical resistivities of the formation layers obtained at (b) toobtain improved vertical resistivities of the formation layers and todetermine corresponding dips thereof; (d) inverting the longitudinalmagnetic dipole measurements, the anisotropy sensitive measurements, andthe symmetrized and anti-symmetrized measurements to update the improvedvertical resistivities obtained at (c) to obtain further improvedvertical resistivities, update the layer boundaries obtained at (a) toobtain improved layer boundaries, and update the dips obtained at (c) toobtain improved dips; and (e) inverting the longitudinal magnetic dipolemeasurements, the anisotropy sensitive measurements, and the symmetrizedand anti-symmetrized measurements to update the horizontal resistivitiesobtained at (a) to obtain improved horizontal resistivities, update theimproved layer boundaries obtained at (d) to obtain further improvedlayer boundaries, and update the improved dips obtained at (d) to obtainfurther improved dips.
 2. The system of claim 1, wherein the processoris capable of determining a quality factor for each of: the improvedhorizontal resistivities obtained at (e), the further improved verticalresistivities obtained at (d), and the further improved dips obtained at(e).
 3. The system of claim 2, wherein the quality factors are definedby model validity, data fit and uncertainty of parameters used ininversion.
 4. The system of claim 3, wherein the quality factors areused to define a confidence level for the improved horizontalresistivities obtained at (e), the further improved verticalresistivities obtained at (d), and the further improved dips obtained at(e).
 5. The system of claim 2, wherein the quality factor is determinedat least partially upon an inversion residual.
 6. The system of claim 2,wherein the quality factor is determined at least partially upon datafit errors and inversion parameter uncertainties.
 7. The system of claim1, wherein the processor is capable of determining a global accuracyvalue for each of: the improved horizontal resistivities obtained at(e), the further improved vertical resistivities obtained at (d), andthe further improved dips obtained at (e).
 8. The system of claim 7,wherein the global accuracy values comprise a weighted average accuracyof the improved horizontal resistivities obtained at (e), the furtherimproved vertical resistivities obtained at (d), and the furtherimproved dips obtained at (e).
 9. The system of claim 1, wherein theelectromagnetic logging tool comprises an electromagnetic inductionlogging tool.
 10. The system of claim 1, wherein the processor iscapable of perturbing at least one of the further improved verticalresistivities obtained at (d), the improved horizontal resistivitiesobtained at (e), the further improved layer boundaries obtained at (e)or the further improved dips obtained at (e), and repeating (d) and (e)until differences between the output of the inversion of thelongitudinal magnetic dipole, anisotropy sensitive, symmetrized andanti-symmetrized channel responses and a measured response of theelectromagnetic logging tool satisfy a selected threshold.
 11. A methodcomprising: using an electromagnetic logging tool to obtainingnon-directional electromagnetic measurements, anisotropy sensitiveelectromagnetic measurements, and directional electromagneticmeasurements in a subsurface formation; (a) determining an initialformation model using at least one of the non-directionalelectromagnetic measurements or the directional electromagneticmeasurements, the initial formation model defining layer boundaries; (b)using the non-directional electromagnetic measurements to invert forhorizontal resistivities and updating the formation model based on thehorizontal resistivities; (c) using the anisotropy sensitiveelectromagnetic measurements to invert for vertical resistivities andupdating the formation model based on the vertical resistivities; (d)using the directional electromagnetic measurements to invert forvertical resistivities that are improved in accuracy relative to thevertical resistivities obtained in (c) and to invert for dip values, andupdating the formation model based on the improved verticalresistivities and the dip values, wherein the directionalelectromagnetic measurements comprise symmetrized and anti-symmetrizedelectromagnetic measurements; (e) using the non-directional,directional, and anisotropy sensitive electromagnetic measurements toinvert for vertical resistivities that are improved in accuracy relativeto the vertical resistivities obtain in (d), to invert for layerboundaries that are improved in accuracy relative to the layerboundaries obtain in (a), and to invert for dip values that are improvedin accuracy relative to the dip values obtained in (d), and updating theformation model based on the improved vertical resistivities, layerboundaries, and dip values; and (f) using the non-directional,directional, and anisotropy sensitive electromagnetic measurements toinvert for horizontal resistivities that are improved in accuracyrelative to the horizontal resistivities obtained in (b), to invert forlayer boundaries that are improved in accuracy relative to the layerboundaries obtained in (e), and to invert for dip values that areimproved in accuracy relative to the dip values obtained in (e), andupdating the formation model based on the improved horizontalresistivities, layer boundaries, and dip values.
 12. The method of claim11, comprising determining a quality factor for each of the horizontalresistivities obtained at (f), the vertical resistivities obtained at(e), and the improved dip values obtained at (f).
 13. The method ofclaim 12, wherein the quality factor is determined at least partiallyupon an inversion residual calculated as a cost function based at leastpartially upon data misfits for measurements used during inversion andregularization terms.
 14. The method of claim 11, comprising conveyingthe electromagnetic logging tool through a borehole formed in thesubsurface formation.
 15. The method of claim 11, comprising perturbingat least one of the horizontal resistivities obtained at (f), thevertical resistivities obtained at (e), the layer boundaries obtained at(f), or the dip values obtained at (f), and repeating (e) and (f) untildifferences between the output of the inversion of the non-directional,anisotropy sensitive, and directional channel responses and a measuredresponse of the electromagnetic logging tool satisfy a selectedthreshold.
 16. The method of claim 11, comprising removing beds from theinitial formation model obtained at (a) that are determined to have athickness below a selected threshold.